Covariant Schwinger Term Research Articles

Covariant Schwinger terms

There exist two versions of the covariant Schwinger term in the literature. They only differ by a sign. However, we shall show that this is an essential difference. We shall carefully (taking all signs into account) review the existing quantum field theoretical computations for the covariant Schwinger term in order to determine the correct expression.

Covariant Stora–Zumino chain terms

In a recent paper, Ekstrand proposed a simple expression from which covariant anomaly, covariant Schwinger term and higher covariant chain terms may be computed. We comment on the relation of his result to the earlier work of Tsutsui.

Chiral and axial anomalies within the framework of generalized canonical quantization

The regularization scheme is proposed for the constrained Hamiltonian formulation of the gauge fields coupled to the chiral or axial fermions. The Schwinger terms in the regularized operator first-class constraint algebra are shown to be consistent with the covariant divergence anomaly of the corresponding current. Regularized quantum master equations are studied, and the Schwinger terms are found out to break down both nilpotency of the BRST-charge and its conservation law. Wess-Zumino consistency conditions are studied for the BRST anomaly and they are shown to contradict to the covariant Schwinger terms in the BRST algebra.

Universal bundle for gravity, local index theorem, and covariant gravitational anomalies

Consistent and covariant Lorentz and diffeomorphism anomalies are investigated in terms of the geometry of the universal bundle for gravity. This bundle is explicitly constructed and its geometrical structure will be studied. By means of the local index theorem for families of Bismut and Freed, the consistent gravitational anomalies are calculated. Covariant gravitational anomalies are shown to be related with secondary characteristic classes of the universal bundle and a new set of descent equations which also contains the covariant Schwinger terms is derived. The relation between consistent and covariant anomalies is studied. Finally a geometrical realization of the gravitational BRS, anti-BRS transformations is presented which enables the formulation of a kind of covariance condition for covariant gravitational anomalies.

On the algebraic structure of covariant anomalies and covariant Schwinger terms

The algebraic structure of covariant anomalies and covariant Schwinger terms in an anomalous Yang-Mills theory is investigated. A cohomological characterization is formulated and geometrically interpreted. A new method of determining covariant anomalies and covariant Schwinger terms based on the BRS-anti-BRS complex is presented.

On the geometrical structure of covariant anomalies in Yang–Mills theory

Covariant anomalies are studied in terms of the theory of secondary characteristic classes of the universal bundle of the Yang–Mills theory. A new set of descent equations is derived which contains the covariant current anomaly and the covariant Schwinger term. The counterterms relating consistent and covariant anomalies are determined. A geometrical realization of the Becchi–Rouet–Stora (BRS)/anti-BRS algebra is presented which is used to understand the relationship between covariant anomalies in different approaches.

Determination of covariant Schwinger terms in anomalous gauge theories

A functional integral method is used to determine equal time commutators between the covariant currents and the covariant Gauss-law operators in theories which are affected by an anomaly. By using a differential geometrical setup we show how the derivation of consistent- and covariant Schwinger terms can be understood on an equal footing. We find a modified consistency condition for the covariant anomaly. As a by-product the Bardeen-Zumino functional, which relates consistent and covariant anomalies, can be interpreted as connection on a certain line bundle over the space of all gauge potentials. Finally the convariant commutator anomalies are calculated for the two- and four dimensional case.

Perturbation Lagrangian Theory for Scalar Fields-Ward-Takahashi Identity and Current Algebra

Under the assumption that the time-ordered products are given by Feynman rules with Bogoliubov's renormalization scheme, it is shown that the operator forms of Euler-Lagrange equations of motion and Noether's theorem for a wide class of perturbation Lagrangian theories for scalar fields are valid. Ward-Takahashi identities for currents in Noether's theorem are also proved without recourse to equal-time commutators, and current-algebra results follow naturally in a subclass of Lagrangian field theories. Covariant Schwinger terms are present in these identities and their nature is determined.

Weinberg sum rules in a perturbation-theoretic model

We examine the Weinberg sum rules in a perturbation theoretic calculation based on the σ-model and find that only the first sum rule is valid. The same is true in a low-order quark-model calculation. A number of constraints on the invariant amplitudes for the three-point function are found to be inconsistent with the perturbation-theory calculation unless we permit either a covariant Schwinger term in the equal-time commutator or include seagull graphs in our model, thus demonstrating their equivalence.

Fubini identities for Feynman diagrams

Fubini-type identities are studied in the Feynman-diagram model of relativitic quantum mechanics using Ward-identity type arguments. Covariant relations with no Schwinger-term contributions are found for currents constructed from Fermi fields, but covariant Schwinger terms are in general present if Bose fields are used to construct the currents. Finally the PCAC assumption is discussed.